[
Barbu, V., Lasiecka, I. and Triggiani, R. (2006) Tangential Boundary Stabilization of Navier-Stokes Equations. Memoirs AMS 181, 852, 128.10.1090/memo/0852
]Search in Google Scholar
[
Bongarti, M., Lasiecka, I. and Rodrigues, J. H. (2022) Boundary stabilization of the linear MGT equation with partially absorbing boundary data and degenerate viscoelasticity. Discrete and Continuous Dynamical Systems, Series S, doi: 10.3934/dcdss.2022020
]Open DOISearch in Google Scholar
[
Bongarti, M., Lasiecka, I. and Triggiani, R. (2022) The SMGTJ equation from the boundary: regularity and stabilization. Applicable Analysis, to appear. doi: 10.1080/00036811.2021.1999420
]Open DOISearch in Google Scholar
[
Bucci, F. and Lasiecka, I. (2019) Feedback control of the acoustic pressure in ultrasonic propagation. Optimization, 68, 10, 1811–1854.10.1080/02331934.2018.1504051
]Search in Google Scholar
[
Clason, C. and Kaltenbacher, B. (2015) Avoiding degeneracy in the Westervelt equation by state constrained optimal control. Evol. Equ. Control Theory 2, 2, 281–300.
]Search in Google Scholar
[
Clason, C., Kaltenbacher, B. and Veljović, S. (2009) Boundary Optimal Control of the Westervelt and the Kuznetsov equations. J. Math. Anal. Appl. 356, 738–751.
]Search in Google Scholar
[
Christov, C. I. and Jordan, P. M. (2005) Heat Conduction Paradox Involving Second-Sound Propagation in Moving Media. Physical Review Letters 94, 15.10.1103/PhysRevLett.94.15430115904151
]Search in Google Scholar
[
Datko, R. (1970) Extending a theorem of Lyapunov to Hilbert spaces. J. Math. Anal. & Appl. 32, 610–616.
]Search in Google Scholar
[
Jordan, P. (2004) An analytical study of Kuznetsov’s equation: diffusive solitons, shock formation, and solution bifurcation. Physics Letters A, 326, 77–84.10.1016/j.physleta.2004.03.067
]Search in Google Scholar
[
Jordan, P. M. (2014) Second-sound phenomena in inviscid, thermally relaxing gases. Discrete Contin. Dyn. Syst. Ser. B 19 7, 2189–2205.
]Search in Google Scholar
[
Jordan, P. M. (2016) The effects of coupling on finite-amplitude acoustic traveling waves in thermoviscous gases: Blackstock’s models. Evol. Equ. Control Theory 5 3, 383–397.10.3934/eect.2016010
]Search in Google Scholar
[
Kaltenbacher, B., Lasiecka, I. and Marchand, R. (2011) Wellposedness and exponential decay rates for the Moore-Gibson-Thompson equations arising in high intensity ultrasound. Control and Cybernetics 40, 4, 971–988.
]Search in Google Scholar
[
Kaltenbacher, B., Lasiecka, I. and Pospieszalska, M. (2012) Well-posedness and exponential decay of the energy in the nonlinear Jordan-Moore-Gibson-Thompson equation arising in high intensity ultrasound. Math. Methods in the Applied Sciences, 22.11, 1250035.10.1142/S0218202512500352
]Search in Google Scholar
[
Kaltenbacher, B. (2015) Mathematics of nonlinear acoustics. Evol. Equ. Control Theory 4, 447–491.
]Search in Google Scholar
[
Lasiecka, I., Lukes, D. and Pandolfi, L. (1995) Input dynamics and nonstandard Riccati equations with applications to boundary control of damped wave and plate equations. J. Optimiz. Theory Appl. 84, 3, 549–574.
]Search in Google Scholar
[
Lasiecka, I., Pandolfi, L. and Triggiani, R. (1997) A singular control approach to highly damped second-order abstract equations and applications. Appl. Math. Optim. 36, 67–107.
]Search in Google Scholar
[
Lasiecka, I. and Triggiani, R. (2000) Control Theory for Partial Differential Equations: Continuous and Approximation Theories, Vol I: Abstract Parabolic Systems; Vol II: Abstract Hyperbolic Systems over a Finite Time Horizon. Encyclopedia of Mathematics and Its Applications Series. Cambridge University Press, January 2000.
]Search in Google Scholar
[
Lasiecka, I. and Triggiani, R. (2022) Optimal feedback arising in a third order dynamics with boundary controls and infinite horizon. J. Opt. Th. & Appl., DOI 10.1007/s10957–022–02017–y.
]Open DOISearch in Google Scholar
[
Louis, D. and Wexler, D. (1991) The Hilbert space regulator and the operator Riccati equation under stabilizability. Annales de la Societé Scientifique de Bruxelles 105, 157–165.
]Search in Google Scholar
[
Moore, F. K. and Gibson, W. E. (1960) Propagation of weak disturbances in a gas subject to relaxation effects. J. Aero/Space Sci., 27, 117–127.
]Search in Google Scholar
[
Marchand, R., McDevitt, T. and Triggiani, R. (2012) An abstract semigroup approach to the third-order MGT equation arising in high-intensity ultrasound: Structural decomposition, spectral analysis, exponential stability. Math. Methods in the Applied Sciences, 35: 1896–1929.10.1002/mma.1576
]Search in Google Scholar
[
Nikolic, V. and Kaltenbacher, B. (2017) Sensitivity analysis for shape optimization of a focusing acoustic lens in lithotripsy. Appl. Math. Optim. 76, 2, 261–301.
]Search in Google Scholar
[
Stokes, G. G. (1851) An examination of the possible effect of the radiation of heat on the propagation of sound. Philosophical Magazine Series, 1(4), 305–317.10.1080/14786445108646736
]Search in Google Scholar
[
Straughan, B. (2010) Acoustic waves in Cattaneo-Christov gas. Physics Letters A 374, 2667-2669.10.1016/j.physleta.2010.04.054
]Search in Google Scholar
[
Thompson, P. A. (1972) Compressible-Fluid Dynamics. McGraw-Hill, New York.10.1115/1.3422684
]Search in Google Scholar
[
Triggiani, R. (1994a) Optimal boundary control and new Riccati equations for highly damped second-order equations. Differential Integral Equations 7, 1109–1144.
]Search in Google Scholar
[
Triggiani, R. (1994b) An optimal quadratic boundary control problem for wave and plate-like equations with high internal damping: An abstract approach. Marcel Dekker Lecture Notes Pure Appl. Math. 165, 215–271. International Conference on Optimal Control for Partial Differential Equations, University of Trento, January 1993.10.1201/9781482277654-89
]Search in Google Scholar
